On sharp reiteration theorems and weighted norm inequalities

We prove sharp end forms of Holmstedt's reiteration theorem which are close ly connected with a general form of Gehring's Lemma. Reverse type condition s for the Hardy-Littlewood-Polya order are considered and the maximal eleme nts are shown to satisfy generalized Gehring conditions. The methods we use are elementary and based on variants of reverse Hardy inequalities for mon otone functions.